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Isomonodromic tau-functions on Hurwitz spaces and their applications

Korotkin, D (Concordia)
Tuesday 22 November 2005, 11:30-12:30

Seminar Room 1, Newton Institute


We discuss Jimbo-Miwa tau-functions corresponding to Riemann-Hilbert problems with quasi-permutation monodromy groups; these tau-functions are sections of certain line bundles on Hurwitz spaces. We show how to compute these tau-functons explicitly in terms of theta-functions and discuss their applications in several areas: large N expansion in Hermitian matrix models, Frobenius manifolds, determinants of laplacians over Riemann surfaces and conformal factor of Ernst equation.


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